CI-groups with respect to ternary relational structures: new examples

TL;DR

This paper investigates conditions under which certain abelian groups are not CI-groups for ternary relational structures, identifying specific groups that satisfy these conditions and determining which are CI-groups for binary and ternary cases.

Contribution

It introduces a sufficient condition for non-CI-groups in ternary structures and classifies which groups of the form Z_2^3×Z_p are CI-groups, also showing Z_2^5 is not.

Findings

Z_3×Z_2^2, Z_7×Z_2^3, Z_5×Z_2^4 are not CI-groups

Complete classification of Z_2^3×Z_p as CI-groups for binary and ternary structures

Z_2^5 is not a CI-group for ternary structures

Abstract

We find a sufficient condition to establish that certain abelian groups are not CI-groups with respect to ternary relational structures, and then show that the groups $\Z_3\times\Z_2^2$, $\Z_7\times\Z_2^3$, and $\Z_5\times\Z_2^4$ satisfy this condition. Then we completely determine which groups $\Z_2^3\times\Z_p$, $p$ a prime, are CI-groups with respect to binary and ternary relational structures. Finally, we show that $\Z_2^5$ is not a CI-group with respect to ternary relational structures.